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arXiv · 2404.13394

The small finitistic dimensions of commutative rings, II

Xiaolei Zhang
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Abstract

The small finitistic dimension $\fPD(R)$ of a ring $R$ is defined to be the supremum of projective dimensions of $R$-modules with finite projective resolutions. In this paper, we investigate the small finitistic dimensions of four types of ring constructions: polynomial rings, formal power series rings, trivial extensions and amalgamations. Besides, we show the small finitistic dimensions of a ring is less than or equal to its Krull dimension. We also give a total ring of quotients with infinite small finitistic dimension.

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Xiaolei Zhang. 2024-04-20. The small finitistic dimensions of commutative rings, II. https://arxiv.org/abs/2404.13394

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